Pressure Reducing 3-Way Valve - MapleSim Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Home : Support : Online Help : MapleSim : MapleSim Component Library : Hydraulics : Valves : Pressure Reducing 3-Way Valve

Pressure Reducing 3-Way Valve

Pressure reducing valve with vent port

Description

The Pressure Reducing 3 Way Valve component models a hydraulic reducing valve as a sharp-edged orifice with the orifice area dependent on the pressure across the valve.

The area varies linearly from ${A}_{\mathrm{open}}$ to ${A}_{\mathrm{close}}$ as the pressure varies from ${p}_{\mathrm{open}}$  to ${p}_{\mathrm{close}}$ and remains at the endpoints for pressures outside this range. The valve can be used to regulate the flow path and vent the outlet port if needed based on the preset pressure setting. The path A-B runs between a pressure reducing valve which will regulate and close the flow path based on the outlet pressure at port B. The path B-C will vent the flow from the outlet port to port C when the pressure exceeds the preset pressure setting in the valve.

Based on the orifice area, the pressure vs. flow rate relationship is calculated using the formulation in the Orifice component.

 Formulation Approaches One of two approaches can be selected for modeling the flow in the device. When the boolean parameter $\mathrm{Use constant Cd}$ is true, a constant coefficient of discharge (${C}_{d}$) is used, otherwise a variable coefficient of discharge with maximum value (${C}_{d\left(\mathrm{max}\right)}$) and a critical flow number (${\mathrm{Crit}}_{\mathrm{no}}$) are used.
 Optional Volumes The boolean parameters $\mathrm{Use volume A}$, $\mathrm{Use volume B}$, and $\mathrm{Use volume C}$ when true, add optional volumes ${V}_{A}$, ${V}_{B}$, and ${V}_{C}$ to ports A, B, and C, respectively. See Port Volumes for details. If two orifices or valves are connected, enabling a volume at the common port reduces the stiffness of the system and improves the solvability.
 Equations ${p}_{\mathrm{AB}}={p}_{A}-{p}_{B}\phantom{\rule[-0.0ex]{3.5ex}{0.0ex}}{P}_{\mathrm{BC}}={p}_{B}-{p}_{C}$ $\mathbf{Orifice Fluid Equations}$ ${q}_{\mathrm{AA}}={u}_{1}{A}_{{\mathrm{cs}}_{1}}\phantom{\rule[-0.0ex]{4.5ex}{0.0ex}}{\mathrm{\Re }}_{1}={u}_{1}\frac{{\mathrm{D}}_{\mathrm{h1}}}{\mathrm{\nu }}$ $\left\{\begin{array}{cc}{p}_{\mathrm{AB}}=\frac{\mathrm{\pi }}{4}\frac{\mathrm{\rho }\mathrm{\nu }{q}_{\mathrm{AA}}}{{C}_{d}^{2}{A}_{{\mathrm{cs}}_{1}}\sqrt{\mathrm{\pi }{A}_{{\mathrm{cs}}_{1}}}}{\left(\frac{16{q}_{\mathrm{AA}}^{4}}{{\mathrm{\pi }}^{2}{A}_{{\mathrm{cs}}_{1}}^{2}{\mathrm{\nu }}^{4}}+{\mathrm{Re}}_{\mathrm{Cr}}^{4}\right)}^{\frac{1}{4}}& \mathrm{Use constant Cd}=\mathrm{true}\\ {q}_{\mathrm{AA}}={C}_{d\left(\mathrm{max}\right)}\mathrm{tanh}\left(4\frac{\sqrt{\frac{{A}_{{\mathrm{cs}}_{1}}}{\mathrm{\pi }}\frac{2\left|{p}_{\mathrm{AB}}\right|}{\mathrm{\rho }}}}{\mathrm{\nu }{\mathrm{Crit}}_{\mathrm{no}}}\right){A}_{{\mathrm{cs}}_{1}}\sqrt{\frac{2\left|{p}_{\mathrm{AB}}\right|}{\mathrm{\rho }}}\mathrm{sign}\left({p}_{\mathrm{AB}}\right)& \mathrm{otherwise}\end{array}$ ${q}_{\mathrm{CC}}={u}_{2}{A}_{{\mathrm{cs}}_{2}}\phantom{\rule[-0.0ex]{4.5ex}{0.0ex}}{\mathrm{\Re }}_{2}={u}_{2}\frac{{\mathrm{D}}_{\mathrm{h2}}}{\mathrm{\nu }}$ $\left\{\begin{array}{cc}{p}_{\mathrm{BC}}=\frac{\mathrm{\pi }}{4}\frac{\mathrm{\rho }\mathrm{\nu }{q}_{\mathrm{CC}}}{{C}_{d}^{2}{A}_{{\mathrm{cs}}_{2}}\sqrt{\mathrm{\pi }{A}_{{\mathrm{cs}}_{2}}}}{\left(\frac{16{q}_{\mathrm{CC}}^{4}}{{\mathrm{\pi }}^{2}{A}_{{\mathrm{cs}}_{2}}^{2}{\mathrm{\nu }}^{4}}+{\mathrm{Re}}_{\mathrm{Cr}}^{4}\right)}^{\frac{1}{4}}& \mathrm{Use constant Cd}=\mathrm{true}\\ {q}_{\mathrm{CC}}={C}_{d\left(\mathrm{max}\right)}\mathrm{tanh}\left(4\frac{\sqrt{\frac{{A}_{{\mathrm{cs}}_{2}}}{\mathrm{\pi }}\frac{2\left|{p}_{\mathrm{BC}}\right|}{\mathrm{\rho }}}}{\mathrm{\nu }{\mathrm{Crit}}_{\mathrm{no}}}\right){A}_{{\mathrm{cs}}_{2}}\sqrt{\frac{2\left|{p}_{\mathrm{BC}}\right|}{\mathrm{\rho }}}\mathrm{sign}\left({p}_{\mathrm{BC}}\right)& \mathrm{otherwise}\end{array}$ $\mathbf{Orifice Area Equations}$ $\left\{\begin{array}{cc}{A}_{{\mathrm{cs}}_{1}}={A}_{i}={A}_{t}& \mathrm{Exact}\\ \left\{{A}_{{\mathrm{cs}}_{1}}=\mathrm{min}\left({A}_{\mathrm{open}},\mathrm{max}\left({A}_{\mathrm{close}},{A}_{i}\right)\right),{t}_{c}\frac{\mathrm{d}{A}_{i}}{\mathrm{d}t}+{A}_{i}={A}_{t}\right\}& \mathrm{otherwise}\end{array}$ ${A}_{t}=\left\{\begin{array}{cc}{A}_{\mathrm{open}}& {p}_{B}<{p}_{\mathrm{open}}\\ {A}_{\mathrm{open}}-\left({A}_{\mathrm{open}}-{A}_{\mathrm{close}}\right)\mathrm{Smooth}\left(S,\frac{{p}_{B}-{p}_{\mathrm{open}}}{{p}_{\mathrm{close}}-{p}_{\mathrm{contrat}}}\right)& {p}_{B}<{p}_{\mathrm{close}}\\ {A}_{\mathrm{close}}& \mathrm{otherwise}\end{array}$ ${A}_{{\mathrm{cs}}_{2}}=\left\{\begin{array}{cc}{A}_{\mathrm{close}}& {p}_{B}<{p}_{\mathrm{open}}\\ {A}_{\mathrm{close}}+\left({A}_{\mathrm{open}}-{A}_{\mathrm{close}}\right)\mathrm{SmoothTrans}\left(S,\left(\frac{{p}_{B}-\left({p}_{\mathrm{close}}+\mathrm{dp}\right)}{{p}_{\mathrm{close}}-{p}_{\mathrm{open}}}\right)\right)& {p}_{B}<2{p}_{\mathrm{close}}+\mathrm{dp}-{p}_{\mathrm{open}}\\ {A}_{\mathrm{open}}& \mathrm{otherwise}\end{array}$ $S=\left\{\begin{array}{cc}\mathrm{smoothness}& \mathrm{smoothTransition}\\ 0& \mathrm{otherwise}\end{array}$ ${p}_{\mathrm{tot}}=p+\left\{\begin{array}{cc}{k}_{p}{p}_{C}& \mathrm{dir}=1\\ -{k}_{p}{p}_{C}& \mathrm{otherwise}\end{array}$ $\mathbf{Optional Volume Equations}$ ${V}_{{f}_{A}}=\left\{\begin{array}{cc}\mathrm{Va}\left(1+\frac{{p}_{A}}{\mathrm{El}}\right)& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{q}_{{V}_{A}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{A}}}{\mathrm{d}t}& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$ ${V}_{{f}_{B}}=\left\{\begin{array}{cc}\mathrm{Vb}\left(1+\frac{{p}_{B}}{\mathrm{El}}\right)& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{q}_{{V}_{B}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{B}}}{\mathrm{d}t}& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$ ${V}_{{f}_{C}}=\left\{\begin{array}{cc}\mathrm{Vb}\left(1+\frac{{p}_{C}}{\mathrm{El}}\right)& \mathrm{Use volume C}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{q}_{{V}_{C}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{C}}}{\mathrm{d}t}& \mathrm{Use volume C}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$ ${q}_{A}+{q}_{B}+{q}_{C}=\phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{q}_{{V}_{A}}+{q}_{{V}_{B}}+{q}_{{V}_{C}}$

Variables

 Name Units Description Modelica ID ${p}_{X}$ $\mathrm{Pa}$ Pressure at port X pX ${p}_{\mathrm{XY}}$ $\mathrm{Pa}$ Pressure drop from X to Y pXY ${q}_{\mathrm{XX}}$ $\frac{{m}^{3}}{s}$ Flow rate into port X qXX ${q}_{{V}_{X}}$ $\frac{{m}^{3}}{s}$ Flow rate into port X's optional volume qVX ${V}_{{f}_{X}}$ ${m}^{3}$ Effective volume at port X VfX ${A}_{{\mathrm{cs}}_{1}}$ ${m}^{2}$ Cross-sectional area from A to B Acs[1] ${A}_{{\mathrm{cs}}_{2}}$ ${m}^{2}$ Cross-sectional area from B to C Acs[2] ${A}_{i}$ ${m}^{2}$ Filtered interpolated area Ai ${A}_{t}$ ${m}^{2}$ Interpolated area At ${u}_{1}$ $\frac{m}{s}$ Fluid velocity from A to B u[1] ${u}_{2}$ $\frac{m}{s}$ Fluid velocity from B to C u[2]

$X,Y\in \left\{A,B,C\right\}$

Connections

 Name Description Modelica ID $\mathrm{portA}$ Upstream hydraulic port portA $\mathrm{portB}$ Downstream hydraulic port portB $\mathrm{portC}$ Venting hydraulic port portC

Parameters

General

 Name Default Units Description Modelica ID ${p}_{\mathrm{close}}$ $2.1·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully closed (A = Aclose) pclose ${p}_{\mathrm{open}}$ $1.9·{10}^{7}$ $\mathrm{Pa}$ Pressure at which the valve is fully open (A = Aopen) popen ${\mathrm{dp}}_{\mathrm{transition}}$ $2.·{10}^{5}$ $\mathrm{Pa}$ Transition pressure between the operation of reducing valve and relief valve dp ${A}_{\mathrm{close}}$ $1·{10}^{-12}$ ${m}^{2}$ Orifice area when closed (leakage) Aclose ${A}_{\mathrm{open}}$ $1·{10}^{-5}$ ${m}^{2}$ Orifice area when fully open Aopen $\mathrm{Exact}$ $\mathrm{false}$ When false (not checked) first-order dynamics are used for the valve area Exact ${t}_{c}$ $0.1$ $s$ Time constant tc $\mathrm{Smooth Transition}$ $\mathrm{false}$ True (checked) means enable the smoothness factor smoothTransition $\mathrm{smoothness}$ $0.5$ Smoothness factor (0: sharpest, 1: smoothest); used when $\mathrm{Smooth Transition}$ is enabled smoothness

Orifice

 Name Default Units Description Modelica ID $\mathrm{Use constant Cd}$ $\mathrm{true}$ True (checked) means a constant coefficient of discharge is implemented, otherwise a variable ${C}_{d}$ is used in flow calculations UseConstantCd ${C}_{d}$ $0.7$ Flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is true Cd ${\mathrm{Re}}_{\mathrm{Cr}}$ $12$ Reynolds number at critical flow; used when $\mathrm{Use constant Cd}$ is true ReCr ${C}_{d\left(\mathrm{max}\right)}$ $0.7$ Maximum flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is false Cd_max ${\mathrm{Crit}}_{\mathrm{no}}$ $1000$ Critical flow number; used when $\mathrm{Use constant Cd}$ is false Crit_no

Optional Volumes

 Name Default Units Description Modelica ID $\mathrm{Use volume A}$ $\mathrm{false}$ True (checked) means a hydraulic volume chamber is added to portA useVolumeA ${V}_{A}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber A Va $\mathrm{Use volume B}$ $\mathrm{false}$ True (checked) means a hydraulic volume chamber is added to portB useVolumeB ${V}_{B}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber B Vb $\mathrm{Use volume C}$ $\mathrm{false}$ True (checked) means a hydraulic volume chamber is added to portC useVolumeC ${V}_{C}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber C Vc

 Name Units Description Modelica ID $\mathrm{\nu }$ $\frac{{m}^{2}}{s}$ Kinematic viscosity of fluid nu $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density of fluid rho $\mathrm{El}$ $\mathrm{Pa}$ Bulk modulus of fluid El